Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics
Kravchenko, Viktor G. ; Kravchenko, Vladislav V.
arXiv, 0305046 / Harvested from arXiv
Text on arXiv
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing non-linear force free magnetic fields or Beltrami fields with nonconstant proportionality factor. 5.The Maxwell equations for slowly changing media. 6.The static Maxwell system. We show that all this variety of first order systems reduces to a single quaternionic equation the analysis of which in its turn reduces to the solution of a Schroedinger equation with biquaternionic potential. In some important situations the biquaternionic potential can be diagonalized and converted into scalar potentials.
Publié le : 2003-05-22
Classification:  Mathematical Physics,  Mathematics - Complex Variables,  30G35,  35Q40,  35Q60 
@article{0305046,
     author = {Kravchenko, Viktor G. and Kravchenko, Vladislav V.},
     title = {Quaternionic factorization of the Schroedinger operator and its
  applications to some first order systems of mathematical physics},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0305046}
}

Kravchenko, Viktor G.; Kravchenko, Vladislav V. Quaternionic factorization of the Schroedinger operator and its
  applications to some first order systems of mathematical physics. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0305046/